Controlling heat flow is a key challenge for applications ranging from thermal management in electronics to energy systems, industrial processing, and thermal therapy. However, progress has generally been limited by slow response times and low tunability in thermal conductance. In this work, we demonstrate an electronically gated solid-state thermal switch using self-assembled molecular junctions to achieve excellent performance at room temperature. In this three-terminal device, heat flow is continuously and reversibly modulated by an electric field through carefully controlled chemical bonding and charge distributions within the molecular interface. The devices have ultrahigh switching speeds above 1 megahertz, have on/off ratios in thermal conductance greater than 1300%, and can be switched more than 1 million times. We anticipate that these advances will generate opportunities in molecular engineering for thermal management systems and thermal circuit design.